The regnant statistical paradigm for database response modeling is: The data analyst fits the data to the presumedly true logistic regression model (LRM), which has the form (equation) of (log of the odds of) response is the sum of weighted predictor variables. The predictor variables are determined by a mixture of well-established variable selection methods and the will of the data analyst to re-express the original variables and construct new variables (data mining). The weights, better known as the regression coefficients, are determined by the pre-programmed machine-crunching method of calculus. The purpose of this article is to show a significant difference for database response modeling when implementing the antithetical machine learning paradigm: The data suggests the “true” model form, as the machine learning process acquires knowledge of the form without being explicitly programmed

I. SituationWhen my daughter Amanda was in grade school, she could not understand the decision-making process of her principal Dr. Katz. On some rainy days, Dr. Katz would permit the class to go outside for recess to play. On other days when it was sunny, Dr. Katz would said, “no play.” As a statistician’s daughter, Amanda collected some weather information, and asked me to build a model to predict what Dr. Katz will do in the days to come. Amanda created a “Let’s Play” database, in Table 1 (also in Quinlan’s C4.5, page 18!), which included the weather conditions for two weeks:

Outlook (sunny, rainy, overcast)

Temperature

Humidity

Windy (yes, no), and of course

Play (yes, no).

I built the easy-to-interpret LRM, and the not-so-easy-to-interpret GenIQ Model for the target variable Play (yes). This creates a counterpoint where the data analyst now can choose between a good interpretable model and a potentially better unexplainable model.

GenIQ variable selection provides a rank-ordering of variable importance for a predictor variable with respect to other predictor variables considered jointly. This is in stark contrast to the well-known, always-used statistical correlation coefficient, which only provides a simple correlation between a predictor variable and the target variable - independent of the other predictor variables under consideration.

Variable Importance (w/r/to other variables considered jointly)

Outlook (overcast)

Outlook (rainy)

Windy (no)

Humidity

Outlook (sunny)

Windy (yes)

Temperature

VI. GenIQ Data MiningGenIQ data mining is directly apparent from the GenIQ tree itself: Each branch is a newly constructed variable, which has power to increase the rank-order predictions.

Var1 = Temperature / Humidity

Var2 = Humidity + Outlook (rainy)

Var3 = Var1 / Var2

Var4 = Outlook (rainy) * Windy (no)

Var5 = Var4 + Outlook (overcast)

GenIQ Model = Var3 + Var5

VII. Play-GenIQ Model ResultsThe results of the Play-GenIQ Model are in Table 3. There is a perfect rank-order prediction of Play.

IIX. Summary

The machine learning paradigm (MLP) “let the data suggest the model” is a practical alternative to the statistical paradigm “fit the data to the LRM equation,” which has its roots when data were only “small.” It was – and still is – reasonable to fit small data to a rigid parametric, assumption-filled model. However, the current information (big data) in, say, cyberspace require a paradigm shift. MLP is a utile approach for database response modeling when dealing with big data, as big data can be difficult to fit in a specified model. Thus, MLP can function alongside the regnant statistical approach when the data – big or small – simply do not “fit.” As demonstrated with the “Let’s Play” data, MLP works well within small data settings.

For more information about this article, call Bruce Ratner at 516.791.3544 or 1 800 DM STAT-1; or e-mail at br@dmstat1.com.